Derive the convergence speed for a dichotomy method for a unimodal function. What type of convergence does this method have?
Consider the function .
Consider the following modification of solution localization method, in which the interval is divided into parts in a fixed proportion of (maximum twice at iteration - as in the dichotomy method). Experiment with different values of and plot the dependence of - the number of iterations needed to achieve - accuracy from the parameter. Consider . Note that with this method is exactly the same as the dichotomy method.
Describe the idea of successive parabolic interpolation. What type of convergence does this method have?